Prigogine was first married to Belgian poet Hélène Jofé (as an author also known as Hélène Prigogine) and in 1945 they had a son Yves. After their divorce, he married Polish-born chemist Maria Prokopowicz (also known as Maria Prigogine) in 1961. In 1970 they had a son Pascal.[14] In 2003 he was one of 22 Nobel Laureates who signed the Humanist Manifesto.[15]

Dissipative structure theory led to pioneering research in self-organizing systems, as well as philosophical inquiries into the formation of complexity on biological entities and the quest for a creative and irreversible role of time in the natural sciences. See the criticism by Joel Keizer and Ronald Fox.

In his later years, his work concentrated on the fundamental role of Indeterminism in nonlinear systems on both the classical and quantum level. Prigogine and coworkers proposed a Liouville space extension of quantum mechanics. A Liouville space is the vector space formed by the set of (self-adjoint) linear operators, equipped with an inner product, that act on a Hilbert space.[17] There exists a mapping of each linear operator into Liouville space, yet not every self-adjoint operator of Liouville space has a counterpart in Hilbert space, and in this sense Liouville space has a richer structure than Hilbert space.[18] The Liouville space extension proposal by Prigogine and co-workers aimed to solve the arrow of time problem of thermodynamics and the measurement problem of quantum mechanics.[19]

Prigogine co-authored several books with Isabelle Stengers, including The End of Certainty and La Nouvelle Alliance (Order out of Chaos).

In his 1996 book, La Fin des certitudes, co-authored by Isabelle Stengers and published in English in 1997 as The End of Certainty: time, chaos, and the new laws of nature, Prigogine contends that determinism is no longer a viable scientific belief. "The more we know about our universe, the more difficult it becomes to believe in determinism." This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations. According to Prigogine, determinism loses its explanatory power in the face of irreversibility and instability.

Prigogine traces the dispute over determinism back to Darwin, whose attempt to explain individual variability according to evolving populations inspired Ludwig Boltzmann to explain the behavior of gases in terms of populations of particles rather than individual particles.[20] This led to the field of statistical mechanics and the realization that gases undergo irreversible processes. In deterministic physics, all processes are time-reversible, meaning that they can proceed backward as well as forward through time. As Prigogine explains, determinism is fundamentally a denial of the arrow of time. With no arrow of time, there is no longer a privileged moment known as the "present," which follows a determined "past" and precedes an undetermined "future." All of time is simply given, with the future as determined or undetermined as the past. With irreversibility, the arrow of time is reintroduced to physics. Prigogine notes numerous examples of irreversibility, including diffusion, radioactive decay, solar radiation, weather and the emergence and evolution of life. Like weather systems, organisms are unstable systems existing far from thermodynamic equilibrium. Instability resists standard deterministic explanation. Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of probability.